MEAN CURVATURE FLOW OF GRAPHS IN ∑1×∑2

摘要

Let ∑1 and ∑2 be m and n dimensional Riemannian manifolds of constant curvature respectively. We assume that w is a unit constant m-form in ∑1 with respect to witch is a graph.We set v=where{e1,…,em}is a normal frame on ∑t Suppose that ∑0 has bounded curvature. If v(x, 0) ≥ v0 ＞√2/2 for all x, then the mean curvature flow has a global solution F under some suitable conditions on the curvatrue of ∑1 and ∑2.